Problem: $A$ $B$ $C$ If: $ AC = 37$, $ BC = 5x + 6$, and $ AB = 2x + 3$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {2x + 3} + {5x + 6} = {37}$ Combine like terms: $ 7x + 9 = {37}$ Subtract $9$ from both sides: $ 7x = 28$ Divide both sides by $7$ to find $x$ $ x = 4$ Substitute $4$ for $x$ in the expression that was given for $BC$ $ BC = 5({4}) + 6$ Simplify: $ {BC = 20 + 6}$ Simplify to find ${BC}$ : $ {BC = 26}$